Space of modular forms of level 1960, weight 2, and trivial character

• Label: 1960.2.a
• Level: $1960$
• Weight: $2$
• Character orbit: 1960.a
• Rep. character: $\chi_{1960}(1,\cdot)$
• Character field: $\Q$
• Dimension: $41$
• Newform subspaces: $25$
• Sturm bound: $672$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 1960 = 2^{3} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1960.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 25 \)
Sturm bound:			\(672\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(3\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1960))\).

	Total	New	Old
Modular forms	368	41	327
Cusp forms	305	41	264
Eisenstein series	63	0	63

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)	\(5\)	\(7\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(+\)	\(5\)
\(+\)	\(+\)	\(-\)	\(-\)	\(6\)
\(+\)	\(-\)	\(+\)	\(-\)	\(7\)
\(+\)	\(-\)	\(-\)	\(+\)	\(3\)
\(-\)	\(+\)	\(+\)	\(-\)	\(4\)
\(-\)	\(+\)	\(-\)	\(+\)	\(6\)
\(-\)	\(-\)	\(+\)	\(+\)	\(4\)
\(-\)	\(-\)	\(-\)	\(-\)	\(6\)
Plus space			\(+\)	\(18\)
Minus space			\(-\)	\(23\)

Trace form

41 * q + 4 * q^3 - q^5 + 33 * q^9 + 2 * q^13 - 14 * q^17 + 8 * q^19 + 4 * q^23 + 41 * q^25 + 16 * q^27 + 2 * q^29 + 24 * q^31 - 24 * q^33 - 2 * q^37 + 8 * q^39 + 2 * q^41 + 8 * q^43 + 3 * q^45 - 20 * q^47 + 8 * q^51 + 14 * q^53 + 4 * q^55 + 8 * q^57 - 8 * q^59 + 18 * q^61 + 10 * q^65 + 40 * q^69 - 16 * q^71 - 6 * q^73 + 4 * q^75 + q^81 + 4 * q^83 + 2 * q^85 + 16 * q^87 + 2 * q^89 + 24 * q^93 - 4 * q^95 - 30 * q^97 + 112 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1960))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces					A-L signs			Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	5	7
1960.2.a.a	$1960$	$2$	1960.a	1.a	$1$	$1$	$1$	$15.651$	\(\Q\)	None	✓				280.2.q.c	$1$	$0$	\(0\)	\(-2\)	\(-1\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-q^{5}+q^{9}-q^{11}-3q^{13}+\cdots\)
1960.2.a.b	$1960$	$2$	1960.a	1.a	$1$	$1$	$1$	$15.651$	\(\Q\)	None	✓	✓			1960.2.a.b	$1$	$1$	\(0\)	\(-2\)	\(-1\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots\)
1960.2.a.c	$1960$	$2$	1960.a	1.a	$1$	$1$	$1$	$15.651$	\(\Q\)	None	✓				280.2.q.b	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-2q^{9}-2q^{11}+4q^{13}+\cdots\)
1960.2.a.d	$1960$	$2$	1960.a	1.a	$1$	$1$	$1$	$15.651$	\(\Q\)	None	✓	✓			1960.2.a.d	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-2q^{9}-5q^{11}-7q^{13}+\cdots\)
1960.2.a.e	$1960$	$2$	1960.a	1.a	$1$	$1$	$1$	$15.651$	\(\Q\)	None	✓				280.2.q.a	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-2q^{9}+2q^{11}-q^{15}+\cdots\)
1960.2.a.f	$1960$	$2$	1960.a	1.a	$1$	$1$	$1$	$15.651$	\(\Q\)	None	✓	✓			1960.2.a.f	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-2q^{9}+3q^{11}+q^{13}+\cdots\)
1960.2.a.g	$1960$	$2$	1960.a	1.a	$1$	$1$	$1$	$15.651$	\(\Q\)	None	✓				40.2.a.a	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-3q^{9}+4q^{11}+2q^{13}-2q^{17}+\cdots\)
1960.2.a.h	$1960$	$2$	1960.a	1.a	$1$	$1$	$1$	$15.651$	\(\Q\)	None	✓	✓			1960.2.a.d	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-2q^{9}-5q^{11}+7q^{13}+\cdots\)
1960.2.a.i	$1960$	$2$	1960.a	1.a	$1$	$1$	$1$	$15.651$	\(\Q\)	None	✓				280.2.q.a	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-2q^{9}+2q^{11}-q^{15}+\cdots\)
1960.2.a.j	$1960$	$2$	1960.a	1.a	$1$	$1$	$1$	$15.651$	\(\Q\)	None	✓	✓			1960.2.a.f	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-2q^{9}+3q^{11}-q^{13}+\cdots\)
1960.2.a.k	$1960$	$2$	1960.a	1.a	$1$	$1$	$1$	$15.651$	\(\Q\)	None	✓				280.2.a.b	$1$	$1$	\(0\)	\(1\)	\(1\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-2q^{9}-5q^{11}-q^{13}+\cdots\)
1960.2.a.l	$1960$	$2$	1960.a	1.a	$1$	$1$	$1$	$15.651$	\(\Q\)	None	✓				280.2.q.b	$1$	$1$	\(0\)	\(1\)	\(1\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-2q^{9}-2q^{11}-4q^{13}+\cdots\)
1960.2.a.m	$1960$	$2$	1960.a	1.a	$1$	$1$	$1$	$15.651$	\(\Q\)	None	✓				280.2.q.c	$1$	$0$	\(0\)	\(2\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+q^{5}+q^{9}-q^{11}+3q^{13}+\cdots\)
1960.2.a.n	$1960$	$2$	1960.a	1.a	$1$	$1$	$1$	$15.651$	\(\Q\)	None	✓	✓			1960.2.a.b	$1$	$0$	\(0\)	\(2\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+q^{5}+q^{9}+4q^{11}+2q^{13}+\cdots\)
1960.2.a.o	$1960$	$2$	1960.a	1.a	$1$	$1$	$1$	$15.651$	\(\Q\)	None	✓				280.2.a.a	$1$	$0$	\(0\)	\(3\)	\(-1\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}-q^{5}+6q^{9}-5q^{11}+5q^{13}+\cdots\)
1960.2.a.p	$1960$	$2$	1960.a	1.a	$1$	$2$	$2$	$15.651$	\(\Q(\sqrt{2}) \)	None	✓				280.2.q.d	$1$	$1$	\(0\)	\(-2\)	\(2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{3}+q^{5}-2\beta q^{9}+(-2+\cdots)q^{11}+\cdots\)
1960.2.a.q	$1960$	$2$	1960.a	1.a	$1$	$2$	$2$	$15.651$	\(\Q(\sqrt{2}) \)	None	✓	✓			1960.2.a.q	$1$	$1$	\(0\)	\(-2\)	\(2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{3}+q^{5}-2\beta q^{9}-q^{11}+\cdots\)
1960.2.a.r	$1960$	$2$	1960.a	1.a	$1$	$2$	$2$	$15.651$	\(\Q(\sqrt{17}) \)	None	✓				280.2.a.d	$1$	$1$	\(0\)	\(-1\)	\(-2\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}-q^{5}+(1+\beta )q^{9}-\beta q^{11}+(-2+\cdots)q^{13}+\cdots\)
1960.2.a.s	$1960$	$2$	1960.a	1.a	$1$	$2$	$2$	$15.651$	\(\Q(\sqrt{33}) \)	None	✓		✓		280.2.a.c	$1$	$0$	\(0\)	\(1\)	\(2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+q^{5}+(5+\beta )q^{9}+(4-\beta )q^{11}+\cdots\)
1960.2.a.t	$1960$	$2$	1960.a	1.a	$1$	$2$	$2$	$15.651$	\(\Q(\sqrt{2}) \)	None	✓				280.2.q.d	$1$	$1$	\(0\)	\(2\)	\(-2\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}-q^{5}+2\beta q^{9}+(-2-2\beta )q^{11}+\cdots\)
1960.2.a.u	$1960$	$2$	1960.a	1.a	$1$	$2$	$2$	$15.651$	\(\Q(\sqrt{2}) \)	None	✓	✓	✓		1960.2.a.q	$1$	$0$	\(0\)	\(2\)	\(-2\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}-q^{5}+2\beta q^{9}-q^{11}+(1+\cdots)q^{13}+\cdots\)
1960.2.a.v	$1960$	$2$	1960.a	1.a	$1$	$3$	$3$	$15.651$	3.3.1944.1	None	✓		✓		280.2.q.e	$1$	$0$	\(0\)	\(0\)	\(-3\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-q^{5}+(3+\beta _{1}+\beta _{2})q^{9}+(1+\cdots)q^{11}+\cdots\)
1960.2.a.w	$1960$	$2$	1960.a	1.a	$1$	$3$	$3$	$15.651$	3.3.1944.1	None	✓				280.2.q.e	$1$	$0$	\(0\)	\(0\)	\(3\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+q^{5}+(3+\beta _{1}+\beta _{2})q^{9}+(1+\cdots)q^{11}+\cdots\)
1960.2.a.x	$1960$	$2$	1960.a	1.a	$1$	$4$	$4$	$15.651$	4.4.16448.2	None	✓	✓	✓		1960.2.a.x	$1$	$1$	\(0\)	\(-2\)	\(-4\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-q^{5}+(1+\beta _{1}+\beta _{2})q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots\)
1960.2.a.y	$1960$	$2$	1960.a	1.a	$1$	$4$	$4$	$15.651$	4.4.16448.2	None	✓	✓	✓		1960.2.a.x	$1$	$0$	\(0\)	\(2\)	\(4\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+q^{5}+(1+\beta _{1}+\beta _{2})q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1960))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1960)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(140))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(196))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(245))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(280))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(392))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(490))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(980))\)\(^{\oplus 2}\)